River networks, which branch like tree limbs across the landscape, are one of Earth’s most widespread and recognizable surface features. They have also been discovered on two other Solar System bodies, Mars and Saturn’s moon Titan. What do these striking landscape patterns tell us about the histories of alien worlds? I will show how mathematical and computational descriptions of slow-acting geological processes, combined with measurements of today’s landscapes, have provided a new perspective on the origin and evolution of river networks. I will then direct your gaze to Titan, where an exotic cocktail of materials and conditions has formed a deceptively Earth-like landscape, and show what our Earthly knowledge can teach us about this mysterious world.